Solve for $x$ and $y$ using elimination. ${4x-y = 5}$ ${3x+4y = 37}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $4$ ${16x-4y = 20}$ $3x+4y = 37$ Add the top and bottom equations together. $19x = 57$ $\dfrac{19x}{{19}} = \dfrac{57}{{19}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {4x-y = 5}\thinspace$ to find $y$ ${4}{(3)}{ - y = 5}$ $12-y = 5$ $12{-12} - y = 5{-12}$ $-y = -7$ $\dfrac{-y}{{-1}} = \dfrac{-7}{{-1}}$ ${y = 7}$ You can also plug ${x = 3}$ into $\thinspace {3x+4y = 37}\thinspace$ and get the same answer for $y$ : ${3}{(3)}{ + 4y = 37}$ ${y = 7}$